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Gröbner basis, Mordell-Weil lattices and deformation of singularities, I
Tetsuji Shioda
Source: Proc. Japan Acad. Ser. A Math. Sci. Volume 86, Number 2 (2010), 21-26.
Abstract
We call a section of an elliptic surface to be everywhere integral if it is disjoint from the zero-section. The set of everywhere integral sections of an elliptic surface is a finite set under a mild condition. We pose the basic problem about this set when the base curve is P1. In the case of a rational elliptic surface, we obtain a complete answer, described in terms of the root lattice E8 and its roots. Our results are related to some problems in Gröbner basis, Mordell-Weil lattices and deformation of singularities, which have served as the motivation and idea of proof as well.
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.pja/1265033217
Digital Object Identifier: doi:10.3792/pjaa.86.21
References
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Digital Object Identifier: doi:10.2969/jmsj/04340673
Project Euclid: euclid.jmsj/1227108034
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